In the simple newsboy model (EZNEWS), presented above, we did not have a fixed ordering charge to deal with. We add this minor complication to the model below. Assuming you decide to order, the fixed charge is a sunk cost and you should therefore order up to the same quantity, S, as in the standard newsboy model. However, there may be cases where preexisting inventory is of a level close enough to S that the expected gains of a minimal increase in inventory are not outweighed by the fixed order charge. The problem now is to not only determine S (or "big S"), but also to determine the additional parameter, s (or "little s"). Where, when inventory exceeds s, the optimal decision is to not incur a fixed charge by foregoing an order for additional stock. Inventory strategies such as this are referred to as "little s-big S", or (s,S), policies.

One additional feature to note in this model is we now assume demand to be normally distributed. This is acceptable because the newsboy model does not demand any particular form of demand distribution. As with the EZNEWS model, we could have also used a Poisson distribution if we felt it was more appropriate.

MODEL:

! Newsboy inventory model;

! This model calculates the optimal stock levels

 for a product with normally distributed demand

 and a fixed ordering cost;

DATA:

P = 11;     ! Penalty/unit for not having enough;

H = 5;      ! Holding cost/unit for excess;

MU = 144;   ! Mean demand;

SIGMA = 25; ! Standard deviation in demand;

K = 15;     ! Fixed cost of placing an order;

ENDDATA

 

! Compute reorder point, SLIL, and order up to

 point, SBIG;

 

! Calculate the order up to point, SBIG, using

 standard newsboy formula;

@PSN( ZBIG ) = P /( P + H);

ZBIG = ( SBIG - MU)/ SIGMA;

 

! and the expected cost of being there, CSBIG;

CSBIG = SIGMA * @PSL( ZBIG) * ( P + H) + H *

 ( SBIG - MU);

 

! The expected cost at the reorder point should

 differ from the expected cost at SBIG by the

 fixed order cost, K;

CSLIL = K + CSBIG;

 

! Solve for SLIL;

CSLIL = SIGMA * @PSL( ZLIL) * ( P + H) * H *

 ( ZLIL * SIGMA);

ZLIL = ( SLIL - MU)/ SIGMA;

 

END

Model: NUSBOY